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C5×(C19⋊C3)⋊Dic29 #45683256

order33060
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C19⋊C3)⋊Dic29
unambiguous semidirect product(C19⋊C3)⋊(C5×Dic29)
unambiguous semidirect productDic551⋊(C3×C5)
unambiguous semidirect product(C5×Dic551)⋊C3

Splittings

derived, HallC19×C29 ⋊ C3×C4×C5
HallC5×Dic551 ⋊ C3
HallC5×C29×C19⋊C3 ⋊ C4
HallC5×C19×C29 ⋊ C3×C4
HallDic551 ⋊ C3×C5
HallC29×C19⋊C3 ⋊ C4×C5
HallC5×C19⋊C3 ⋊ Dic29
HallC5×C29 ⋊ (C19⋊C3)⋊C4
HallC5×C19 ⋊ C3×Dic29
HallC19⋊C3 ⋊ C5×Dic29
SylowC29 ⋊ C5×(C19⋊C3)⋊C4
SylowC19 ⋊ C3×C5×Dic29

Subgroups

subgroupG/H
center, hypercenterC2×C5C29⋊(D19⋊C3)
commutator, hypocenterC19×C29C3×C4×C5
FrattiniC2C5×C29⋊(D19⋊C3)
Fitting, socleC2×C5×C19×C29C2×C3
prime radicalC2×C5×C29×C19⋊C3C2
cosocleC2×C19×C29C2×C3×C5
LCSG ▷ C19×C29
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11020

Conjugacy classes & character table

1350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 20);